The present invention relates to a method and apparatus for performing address transformation of projection data for use in a positron computed tomographic system and more particularly, to a method and apparatus for performing address transformation of the projection data for use in a positron CT system using the addresses of a pair of detector groups including two detectors that have detected coincidently gamma-rays, and the addresses of these detectors in their respective groups.
The recent advances in a CT system have been remarkable, and X-ray and ultrasonic CT systems and other similar systems are being used with great advantage in hospitals and research laboratories for various purposes including diagnosis of diseases and examination of organs and tissues in the living body. Among the CT systems available today, positron CT systems are being studied most extensively and hold much promise for future applications.
A positron CT system comprises a plurality of detectors that are arrayed in an annular or polygonal form around the patient. When a tracer radionuclide (i.e. isotope) is injected into the body of the patient, the isotope emits a positron upon disintegration, which binds almost instantly with an electron in the body, resulting through pair annihilation in the simultaneous emission of two gamma-rays moving in nearly opposite directions. When a pair of detectors recognizes coincident events of gamma-ray emission, that is, detects coincidentally the gamma-rays, the point of isotope disintegration is determined to lie on a line joining the two detectors. In this case, each of the addresses assigned to the two detectors is transformed in an address transforming circuit to projection data address (T, .theta.), which is used in image reconstruction process, and then stored in the memory or disk of a computer.
The projection data addresses will be explained hereinafter with reference to FIG. 1.
As shown in FIG. 1, gamma-ray detectors D.sub.i-1, D.sub.i-2, D.sub.i-3, . . D.sub.j-1, D.sub.j-2, D.sub.j-3, . . . are arranged, for example, in an annular form. Assuming that .theta. is the angle of inclination of the line which passes the center 0 of the ring and vertically intersects the line joining two detectors (D.sub.i-2 and D.sub.j-2 in FIG. 1) and T is the length of the perpendicular (i.e., the distance between the center 0 and the line joining D.sub.i-2 and D.sub.j-2), the addresses (#i, #j) assigned to the paired detectors are transformed to the corresponding polar coordinates (T, .theta.), and the addresses thus obtained are used as projection data addresses in the image reconstruction process.
As shown in FIG. 2, the detectors are usually classified into a plurality of groups (G1, G2 . . . , G.phi.) each of which includes N detectors, and each pair of detectors is assigned two types of addresses, one of which is the address (G.sub.i, G.sub.j) of the group including each of the paired detectors and the other of which is the address (Xi, Xj) of a detector defined in a group. That is, an absolute address (#i, #j) of the paired detectors can be represented by the two types of the addresses (G.sub.i, G.sub.j) and (X.sub.i, X.sub.j). Detection of coincident events of gamma ray emission is also performed between detector groups. When detection of the coincident events is accomplished with two detectors that is, the gamma-rays has been coincidentally detected by the paired detectors, the addresses (G.sub.i, G.sub.j) of the groups including the paired detectors and the addresses (X.sub.i, X.sub.j) of the paired detectors defined in the respective groups are supplied into an address transforming circuit, where they are transformed to projection data addresses (T, .theta.). To this end, a look-up table representing the relationship between detector addresses (G.sub.i, G.sub.j, X.sub.i, X.sub.j) and (T, .theta.) addresses is preliminarily stored in a semiconductor memory ROM or RAM and transformation is performed by use of this table.
A prior art address transforming circuit as shown in FIG. 6 consists basically of a memory 1' for storing a value corresponding to T (the length of the line which passes the center 0 and vertically intersects the line joining paired detectors) and a memory 2' for storing a value corresponding to the angle .theta. of inclination of the normal line with respect to a predetermined line (e.g., a dotted line as shown in FIG. 1). Signals representing the addresses (G.sub.i, G.sub.j) of the groups to which paired detectors belong and the addresses (X.sub.i, X.sub.j) of the detectors defined in the respective groups are inputted through input lines to the memories and the corresponding (T, .theta.) addresses are outputted.
The prior art address transforming circuit, however, has a serious drawback in that the number of addresses that can be received by IC memories is limited; for example, a commonly employed 256 kb ROM can receive only 15 bits (over 15 input lines) and output 8 bits (over 8 output lines). In other words, if many detectors are used in the prior art method, all inputs of (G.sub.i, G.sub.j, X.sub.i and X.sub.j) cannot be received by a single IC memory and therefore additional memories must be connected in parallel in order to absorb the extra number of bits in (G.sub.i +G.sub.j +X.sub.i +X.sub.j) which can not be received by a single memory. If a 256 kb ROM is used for signals representing G.sub.i and G.sub.j each compound of 4 bits and X.sub.i and X.sub.j each composed of 6 bits, 32 IC memories are necessary since 2(4+4+6+6)-15=32. Accordingly, the prior art address transforming circuit causes a high cost product.